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TITLE
DECLARATION
ACKNOWLEDGEMENT
DEDICATION
ABSTRACT
PREFACE
List of Publications
CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF APPENDICES
1. A BRIEF REVIEW ON THE TRIGONAL CRYSTALS CaCO3, Bi AND LiNbO3 AND AN INTRODUCTIONTO THE FINITE STRAIN ELASTICITY THEORY
1.1 Introduction
1.2 Calcite
1.3 Bismuth
1.4 Lithium Niobate
1.5 The Theory of Elasticity
1.6 Finite Strain Theory of Elasticity
References:
2. KEATING’S APPROACH TO THE LATTICE DYNAMICS, SECOND AND THIRD-ORDER ELASTIC CONSTANTS AND PRESSURE DERIVATIVES OF THE SECOND-ORDER ELASTIC CONSTANTS OF TRIGONAL CRYSTALS
2.1 Introduction
2.2 Keating’s Approach to the Lattice Dynamics
2.3 Calculation of the Second and Third-Order ElasticConstants by the Method of Homogeneous Deformation
2.4 Calculation of the Pressure Derivatives of the Second-OrderElastic Constants of Trigonal Crystals
References:
3. QUASI-HARMONIC THEORY OFTHERMAL EXPANSION AND THE LOWTEMPERATURE LIMIT γL OF THE GRUNEISEN FUNCTION
3.1 Introduction
3.2 Quasi-Harmonic Theory of Thermal Expansion
3.3 Procedure to Calculate the Low Temperature Limit of the Gruneisen Function (y2)
References:
4. SECOND-ORDER ELASTIC CONSTANTS, THIRD-ORDER ELASTIC CONSTANTS, PRESSURE DERIVATIVES OF THE SECOND-ORDER ELASTIC CONSTANTS AND LOW TEMPERATURE THERMAL EXPANSION OF CaCO3
4.1 Introduction
4.2 Second-Order Elastic Constants of CaCO3
Table 4.1Values of second-order potential parameters (in GPa) of CaCO3
Table 4.2Second-order elastic constants (in GPa) of CaCO3
4.3 Third-Order Elastic Constants of CaCO3
Table 4.3Values of third-order potential parameters (in GPa) of CaCO3
Table 4.4Third-order elastic constants (in GPa) of CaCO3
4.4 Pressure Derivatives of the Second-Order Elastic Constantsof CaCO3
Table 4.5Pressure derivatives of the second-order elasticconstants of CaCO3
4.5 Generalized Gruneisen Parameters of Elastic Waves andLow Temperature Thermal Expansion
Table 4.6Generalized Gruneisen parameters of the elastic wavespropagating at different angles to the unique axis in CaCO3
Fig.4.1: Variation of the acoustic wave velocities with angle tothe unique axis of CaCO3.
Fig.4.2: Variation of the generalized Gruneisen parameters g ¢jwith angle for the different acoustic modes in CaCO3.
Fig.4.3: Variation of the generalized Gruneisen parameters g ¢j¢with angle for the different acoustic modes in CaCO3.
4.6 Results and Discussion
References:
5. SECOND-ORDER ELASTIC CONSTANTS, THIRD-ORDERELASTIC CONSTANTS, PRESSURE DERIVATIVES OF THESECOND-ORDER ELASTIC CONSTANTS AND LOWTEMPERATURE THERMAL EXPANSION OF TRIGONAL Bi
5.1 Introduction
5.2 Second and Third-Order Elastic Constants of Bi
Table 5.IValues of second-order potential parameters (in GPa) of Bi
Table 5.2Second-order elastic constants (in GPa) of Bi
5.3 Third-Order Elastic Constants of Bi
Table 5.3Values of third-order potential parameters (in GPa) of Bi
Table 5.4Third-order elastic constants (in GPa) of Bi
5.4 Pressure Derivatives of the Second-Order Elastic Constantsof Bi
Table 5.5Pressure derivatives of the second-order elastic constants of Bi
5.5 Generalized Gruneisen Parameters of Elastic Waves andLow Temperature Thermal Expansion
Table 5.6Generalized Gruneisen parameters of the elastic wavespropagating at different angles to the unique axis in Bi
Fig.5.1: Variation of the acoustic wave velocities with angle tothe unique axis of Bi
Fig.5.2: Variation of the generalized Gruneisen parameter j g ¢ withangle for the different acoustic modes in Bi
Fig.5.3: Variation of the generalized Gruneisen parameter j g ¢¢ withangle for the different acoustic modes in Bi
5.6 Results and Discussion
References
6. SECOND-ORDER ELASTIC CONSTANTS, THIRD-ORDER ELASTIC CONSTANTS, PRESSURE DERIVATIVES OF THE SECOND-ORDER ELASTIC CONSTANTS AND LOW TEMPERATURE THERMAL EXPANSION OF TRIGONAL LiNbO3
6.1 Introduction
6.2 Second-Order Elastic Constants
Table 6.1Values of second-order potential parameters (in GPa) of LiNbO3
Table 6.2Second-order elastic constants (in GPa) of LiNbO3
6.3 Third-Order Elastic Constants
Table 6.3Values of third-order potential parameters (in GPa) of LiNbO3
Table 6.4Third-order elastic constants (in GPa) of LiNbO3
6.4 Pressure Derivatives of the Second-Order Elastic Constants
Table 6.5Pressure derivatives of the second-order elastic constants ofLiNbO3
6.5 Generalized Gruneisen Parameters of Elastic Waves andLow Temperature Thermal Expansion
Table 6.6Generalized Gruneisen parameters of the elastic wavespropagating at different angles to the unique axis in LiNbO3
Fig.6.1: Variation of the acoustic wave velocities with angle tothe unique axis of LiNbO3
Fig.6.2: Variation of the generalized Gruneisen parameters j g ¢ withangle for the different acoustic modes in LiNbO3
Fig.6.3: Variation of the generalized Gruneisen parameters j g ¢¢with angle for the different acoustic modes in LiNbO3
6.6 Results and Discussion
References:
7. SUMMARY AND CONCLUSION
References
APPENDIX I Position co-ordinates of the Three nearest neighbours of the different atoms in the unit cell of CaCO3
APPENDIX II Position co-ordinates of the Three nearest neighbours of the different atoms in the unit cell of Bi
APPENDIX III Position co-ordinates of the Three nearest neighbours of the different atoms in the unit cell of LiNbO3